a corporation must appoint a president, chief executive officer (ceo), chief operating officer (coo), and…

a corporation must appoint a president, chief executive officer (ceo), chief operating officer (coo), and chief financial officer (cfo). it must also appoint a planning committee with four different members. there are 15 qualified candidates, and officers can also serve on the committee. complete parts (a) through (c) below.\na. how many different ways can the four officers be appointed?\nthere are different ways to appoint the four officers.

a corporation must appoint a president, chief executive officer (ceo), chief operating officer (coo), and chief financial officer (cfo). it must also appoint a planning committee with four different members. there are 15 qualified candidates, and officers can also serve on the committee. complete parts (a) through (c) below.\na. how many different ways can the four officers be appointed?\nthere are different ways to appoint the four officers.

Answer

Explanation:

Step1: Identify permutation formula

The number of permutations of $n$ objects taken $r$ at a time is $P(n,r)=\frac{n!}{(n - r)!}$. Here $n = 15$ (number of candidates) and $r=4$ (number of officer - positions).

Step2: Calculate factorial values

$n!=n\times(n - 1)\times\cdots\times1$. So, $P(15,4)=\frac{15!}{(15 - 4)!}=\frac{15!}{11!}$. Since $15! = 15\times14\times13\times12\times11!$, then $P(15,4)=15\times14\times13\times12$.

Step3: Perform multiplication

$15\times14 = 210$, $210\times13=2730$, $2730\times12 = 32760$.

Answer:

$32760$